example 5
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EXAMPLE 5 Find leg lengths using an angle of elevation
SKATEBOARD RAMP
You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You need to find the height and length of the base of the ramp.
EXAMPLE 5 Find leg lengths using an angle of elevation
SOLUTION
sin 26o=
opp. hyp. Write ratio for sine of 26o.
sin 26o x
=14 Substitute.
14 sin 26o = x Multiply each side by 14.
6.1 x Use a calculator to simplify.
STEP 1 Find the height.
ANSWER The height is about 6.1 feet.
EXAMPLE 5 Find leg lengths using an angle of elevation
cos 26o=
adj. hyp. Write ratio for cosine of 26o.
cos 26o y
=14 Substitute.
14 cos 26o = y Multiply each side by 14.
12.6 y Use a calculator to simplify.
STEP 2 Find the length of the base.
ANSWER The length of the base is about 12.6 feet.
EXAMPLE 6 Use a special right triangle to find a sine and cosine
Use a special right triangle to find the sine and cosine of a 60o angle.
SOLUTION
sin 60o =opp. hyp.
=3
20.08660
cos 60o =adj. hyp.
=21
0.5000=
Use the 30o - 60o - 90o Triangle Theorem to draw a right triangle with side lengths of 1, , and 2. Then set up sine and cosine ratios for the 60o angle.
3
GUIDED PRACTICE for Examples 5 and 6
7. WHAT IF?
In Example 5, suppose the angle of elevation is 35o. What is the new height and base length of the ramp?
ANSWER about 8 feet, about 11.5 ft
8. Use a special right triangle to find the sine and cosine of a 30o angle.
ANSWER 1 2
,23
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